The list includes Spain, Portugal, Cyprus and Greece.
Greek tourism minister Harry Theocharis has suggested the nation is open to making a deal directly with the UK for travel, regardless of EU decisions.
Mr Theocharis said: “I have to be categorical that bilateral or multilateral deal aside – it doesn’t matter – the UK will be open to Greece.”
However, the nation added it could soon welcome travellers back to the Canary and Balearic Islands as long as they can produce a negative COVID-19 test result.
Cyprus’ government additionally stated that they will welcome tourists to the nation if they have received both doses of the coronavirus vaccine.
Meanwhile, Rita Marques, Portugal’s tourism minister has expressed her hopes for the country to soon open its borders to tourists who have either been vaccinated or tested negative for the coronavirus.
Despite progress towards travel, for the time being, Britons can not travel for leisure.
If Prime Minister Boris Johnson’s “roadmap” out of lockdown goes to plan holidaymakers could be jetting off from May 17.
However, this is dependent on the Covid data across the country at that time.